Best Known (94, 94+22, s)-Nets in Base 9
(94, 94+22, 48314)-Net over F9 — Constructive and digital
Digital (94, 116, 48314)-net over F9, using
- net defined by OOA [i] based on linear OOA(9116, 48314, F9, 22, 22) (dual of [(48314, 22), 1062792, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9116, 531454, F9, 22) (dual of [531454, 531338, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(91, 13, F9, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- OA 11-folding and stacking [i] based on linear OA(9116, 531454, F9, 22) (dual of [531454, 531338, 23]-code), using
(94, 94+22, 318489)-Net over F9 — Digital
Digital (94, 116, 318489)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9116, 318489, F9, 22) (dual of [318489, 318373, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9116, 531454, F9, 22) (dual of [531454, 531338, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(91, 13, F9, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(9116, 531454, F9, 22) (dual of [531454, 531338, 23]-code), using
(94, 94+22, large)-Net in Base 9 — Upper bound on s
There is no (94, 116, large)-net in base 9, because
- 20 times m-reduction [i] would yield (94, 96, large)-net in base 9, but